Advances in Fingerprint Technology.pdf

Galton continued, making a further assumption:
… when the surrounding conditions alone are taken into account, the ridges
within their limits may either run in the observed way or in a different way,
the chance of these two contrasted events being taken (for safety’s sake) as
approximately equal.
The weakness of Galton’s model lies in the magnitude of the above
approximation and in the arbitrary value chosen for Factor C. One can justly
criticize his final figure as a gross underestimate of fingerprint variability.
Pearson’s calculations of the variability in one of Galton’s regions may be
closer to reality, but both his hypothesis and Galton’s remain untested.
The Henry-Balthazard Models (1900–1943)
Description of the Henry-Balthazard Models
The Henry-Balthazard approach is used in six closely related, fairly simplistic
models for fingerprint individuality. Each employs a fixed probability P for
the occurrence of one minutia. Assuming independence of these occurrences,
the models calculate the probability of a particular configuration of N minutiae
using Equation (9.4):
P(C) = (P) N (9.4)
Henry 15 was the first to use this approach in 1900, and Balthazard 16 in
1911 made the most extensive analysis. Minor variations are encountered in
the works of Bose, 30 Wentworth and Wilder, 31 Cummins and Midlo, 32 and
Gupta. 33
Henry Model (1900)
Henry 15 chose an arbitrary probability of one fourth for the occurrence of
each minutia, as well as for the general pattern type, and the core-to-delta
ridge count. To use his method, one counts the number of minutiae; if the
pattern type is discernable, one adds two minutia equivalents. This value is
used as N, with 1/4 as P.
Balthazard Model (1911)
Balthazard’s method 16 is particularly important because it is the historical
basis for widely accepted rules regarding fingerprint individuality. Balthazard
assumed that for each minutia, there were four possible events: